This answer is courtesy of Douglas A. Biesecker, School of Physics and
Space Research, University of Birmingham, UK.
The size of a solar flare is actually a difficult question to answer. If what we want to know is what will the effect at Earth be, then we want to know the total number of photons and the total number of particles of different energies that will strike the Earth's atmosphere. The actual volume the flare occurs in, or the size in miles, is not important.
A flare emits photons, and sometimes particles, from the Sun, which sometimes reach the Earth. Whether or not they reach the Earth does not depend on the size of the flare, but depends only on where on the Sun the flare occurred.
Fortunately, no matter what, flares do not have a significant effect on us here on Earth. The Earth's atmosphere more or less acts as a shield to prevent the cosmic radiation from reaching us. There can be measurable effects at ground level, but the amount of radiation is pretty insignificant.
The largest flare ever recorded was in August, 1972. That flare has had no discernible effects on any terrestrial populations, including people.
What sort of fluxes would have to strike the Earth to wipe us
out? I don't know the answer to that, but obviously, we've never even
observed a solar event big enough to have any measurable effects on human
health. It is also unlikely that the Sun could produce such a flare.
(Amara Graps, adding to the above.)
Solar scientists are very much interested in forecasting active magnetic disturbances, in particular, the flares that arise out of active regions. They run complex code that models the magnetic field of the Sun. But it is very much like weather forecasting, an imprecise science. So they can give probabilities, based on their model results, only.
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